Two identical wheeled carts of mass m are
connected between two walls as shown in the figure below. The inner
spring has spring constant k and
the two outer springs have spring constants K = 10k. All
three springs have a rest length l0 and the distance between the
walls is L.

(a) Choose a convenient coordinate system for describing the positions
of the carts and write the equations of motion for the carts. Be
sure to specify your coordinate system.

(b) Describe what the normal modes will be like.

(c) Find the normal modes and normal frequencies (expressed as a function
of )
using any approach you want.